prediktionsinterval

A prediction interval is a statistical range that is likely to contain a future observation from a random process. Unlike a confidence interval, which estimates the range of possible values for a population parameter, a prediction interval estimates the range for a single future data point. It accounts for both the uncertainty in estimating the model parameters (like the mean and variance) and the inherent variability of the data itself.

The width of a prediction interval depends on several factors. A larger sample size generally leads to narrower intervals as the parameter estimates become more precise. Higher variability in the data (a larger standard deviation) will result in wider intervals. The desired confidence level also plays a role; a higher confidence level (e.g., 95% versus 90%) will require a wider interval to capture more of the potential outcomes.

Prediction intervals are commonly used in forecasting and quality control. For example, a company might use a prediction interval to estimate the range of sales for the next quarter, or a manufacturer might use one to predict the lifespan of a product. It is important to remember that a prediction interval provides a probabilistic statement about a future observation, not a guarantee.